1. **State the problem:** Solve for $x$ in the equation $3 - 14x = 17$. 2. **Isolate the term with $x$:** Subtract 3 from both sides to get the term with $x$ alone. $$3 - 14x - 3 = 17 - 3$$ $$-14x = 14$$ 3. **Divide both sides by the coefficient of $x$:** To solve for $x$, divide both sides by $-14$. $$x = \frac{14}{-14}$$ 4. **Simplify the fraction:** $$x = \cancel{\frac{14}{-14}} = -1$$ 5. **Final answer:** $$\boxed{-1}$$